An important feature of state-of-the-art and newly emerging communication systems (e.g. enhanced so-called third generation and later generation wireless telecommunication systems according to the third generation partnership program for the universal mobile telecommunication system) is a capability of both wireless transmitters and receivers to adapt their functionality and parameters according to prevailing channel conditions. Channel conditions in mobile communications change for example because as a mobile station changes location and as objects that scatter a mobile signal move about, the communication signal between the mobile station and the base station is differently reflected, refracted, and diffracted, giving rise to different multiple indirect paths linking the mobile and the base station with which the mobile is in communication. Thus, a signal transmitted by a transmitter at either a base station or a mobile terminal undergoes distortion (change in amplitude and phase) due to changing destructive interference among changing multiple propagation paths to a receiver, in what is known as (time-varying) multipath fading. As opposed to line of sight communication systems, mobile channels tend to have a large number of indirect paths, and to have different indirect paths at different times. In addition to fading, a signal will also experience dispersion, defined as spreading of the signal in time or frequency. Thus, mobile channels are typically fading dispersive communication channels.
In characterizing a fading dispersive channel so as to allow both transmitter and receiver to adapt to changing channel conditions, it is typically assumed that the response of the channel to a unit impulse is quasi-stationary, i.e. although the fluctuations in the channel are due to non-stationary statistical phenomena, on a short enough time scale and for small enough bandwidth, the fluctuations in time and frequency can be characterized as approximately stationary. For characterizing a mobile channel over short time periods, such as in determining short term fading, it is usually assumed that the channel impulse response is stationary in time, or in other words, that the channel is wide-sense stationary (WSS). In addition, it is often assumed that the channel impulse response is independent for different values of delay, in which case the channel is said to exhibit uncorrelated scattering of the transmitted signal. When a time-varying impulse response is assumed to have stationary fluctuations in time and frequency, the channel is said to be wide-sense stationary with uncorrelated scattering (WSSUS). A (statistical) model of a WSSUS channel requires only two sets of parameters to characterize fading and multipath effects: a power delay profile (PDP) parameter set and a Doppler power spectra (DPS) parameter set.
A WSSUS channel (in which, e.g. fading multipath occurs) can be characterized by a so-called scattering function S(τ,ƒ), where τ denotes delay of an indirect path compared to the direct (mobile channel) path, and where ƒ denotes the frequency. The scattering function S(τ,ƒ) is the double Fourier transform of the so-called spaced-frequency, spaced-time (auto) correlation function rHH(Δƒ,Δt) of the Fourier transform of the channel impulse response, i.e.             S      ⁡              (                  τ          ,          f                )              =                  ∫                  -          ∞                ∞            ⁢                        ∫                      -            ∞                    ∞                ⁢                                            r              HH                        ⁡                          (                                                Δ                  ⁢                                                                           ⁢                  f                                ,                                  Δ                  ⁢                                                                           ⁢                  t                                            )                                ⁢                      ⅇ                                          j2π                ·                Δ                            ⁢                                                           ⁢                              f                ·                τ                                              ⁢                      ⅇ                                                            -                  j2π                                ·                f                ·                Δ                            ⁢                                                           ⁢              t                                ⁢                                           ⁢                      ⅆ                          (                              Δ                ⁢                                                                   ⁢                f                            )                                ⁢                                           ⁢                      ⅆ                          (                              Δ                ⁢                                                                   ⁢                t                            )                                            ,where                     r        HH            ⁡              (                              Δ            ⁢                                                   ⁢            f                    ,                      Δ            ⁢                                                   ⁢            t                          )              =                  1        2            ⁢      E      ⁢              {                  H          *                                    (                              f                ,                t                            )                        ·                          H              ⁡                              (                                                      f                    +                                          Δ                      ⁢                                                                                           ⁢                      f                                                        ,                                      t                    +                                          Δ                      ⁢                                                                                           ⁢                      t                                                                      )                                                    }              ,where E{. . . } is the mathematical expectation of the indicated argument, and in which H(ƒ,t) is the Fourier transform of the channel impulse response function. The PDP and DPS parameter sets are defined by integration of the scattering function, as follows:                     PDP        ⁡                  (          τ          )                    =                        ∫                      -                          F                              D                max                                                          +                          F                              D                max                                                    ⁢                              S            ⁡                          (                              τ                ,                f                            )                                ⁢                                           ⁢                      ⅆ            f                                ,                   ⁢    and              DPS      ⁡              (        f        )              =                  ∫        0                  τ          max                    ⁢                        S          ⁡                      (                          τ              ,              f                        )                          ⁢                                   ⁢                              ⅆ            τ                    .                    The scattering function has the dimensions of power density. An example of a scattering function for a time varying channel is shown in FIG. 1.
Thus, because the scattering function includes information about how a communication channel varies in time and how it depends on the frequency of the transmitted signal, it includes information on (sufficient to determine) what is here called the (carrier frequency) offset Ω (also sometimes called the Doppler shift), i.e. the positive or negative change in carrier frequency of the transmitted signal due to dispersion (caused e.g. by Doppler scattering of the communication channel by moving objects in the communication channel) and the transmitter and receiver oscillator instabilities, and it also includes information on what is called the fading rate ν—the product of the time interval T between when successive symbols are received and the bandwidth of the Doppler spectrum (called also a Doppler spread) ƒD (so that ν≡ƒDT). The offset as used here is the total difference between the carrier frequency of the transmitted signal or a related frequency and a local frequency at which a (local) oscillator in the receiver oscillates—an oscillator originally tuned to (either) the carrier frequency (or an appropriate related frequency), i.e. initially tuned to a frequency suitable for receiving the carrier frequency. The frequency of the local oscillator can differ from the carrier frequency (or a related frequency) by the offset as the communication channel changes and/or the local oscillator in the transmitter or in the receiver exhibits a frequency drift. The frequency offset effectively causes a shift in the center frequency of the Doppler spectrum. The fading rate ν=ƒDT (sometimes called a normalized Doppler spread) denotes what can be considered a bandwidth (normalized by T) of the received signal when a single tone is transmitted, i.e., a bandwidth of the Doppler spectrum (with T the time interval between successive symbols, as defined above). The Doppler spread ƒD is normalized with 1/T (bandwidth of the data signal) so that the quantity ν=ƒDT measures the relation between the bandwidths of the data signal and the Doppler spread caused by the channel.
Note that the local oscillator is only tuned to the carrier frequency (as opposed to a related frequency) in direct conversion receivers. As indicated above in respect to the offset, the invention is equally feasible for heterodyne receivers using intermediate frequencies (IF). In such receivers, the local oscillator is not tuned to the carrier frequency (fc) but is instead tuned to a related frequency, one that differs from the carrier frequency by the IF (i.e. either fc−IF or fc+IF).
For sampled received signals, the multipath fading channel can be described with a discrete-time tapped-delay-line model, such as shown in FIG. 5, where fading process ƒi,k for each tap is described with the first-order autoregressive lowpass process but the extension to higher-order models is straightforward. The scattering function for the discrete-time channel model is sampled in delay, as shown in FIG. 6. The discrete-time channel model is characterized by a discrete number of signal paths where at each path the transmitted signal experience some delay and multiplicative distortion, i.e., at each signal path the delayed version of the transmitted signal is multiplied by a time-varying fading coefficient and by a rotator that is rotating at the speed of the Doppler (shift) frequency. Each time-varying fading coefficient ƒi,k can be modelled as a low-pass random process with a bandwidth νi (called here a fading rate). The fading rate and Doppler frequency (carrier frequency offset) can in general be different for different resolvable multipath signals (for each channel tap). (In fact, from the physical modeling point of view, each resolvable multipath signal itself is also composed of a large number of separate multipath signals that experience approximately same delay, i.e., the difference in the delay between these multipath signal components is less than the symbol period. Therefore, each resolvable multipath signal can be regarded as a cluster of many multipath signal components with about the same delay and which sum up either constructively or destructively at any time instant, thus creating what is called here a fading channel tap. The difference in delay between any pair of resolvable multipath signals (any pair of channel taps) is equal to T or greater.) Therefore, it is important that the fading rate and offset be estimated for each resolvable multipath component of the received signal (for each channel tap) separately.
A statistically equivalent discrete-time channel model is presented in FIG. 7. The first-order AR-coefficients are in this model defined as ai=a′iexp(j2πΩ) (for i=1 . . . L) (but the extension to higher-order models is again straightforward). Thus, the originally lowpass fading process ƒi,k with the bandwidth determined by a′i is effectively converted to the complex bandpass process having a center frequency Ωi and the same bandwidth as the equivalent lowpass process. (In fact, the original lowpass fading process is only shifted in frequency by Ωi). The main advantage of this channel model over the model described in FIG. 5 is that the modified AR-coefficients (matrix A) now includes information about both the bandwidth of the fading process (fading rate) and the Doppler (shift) frequency (frequency offset) in each channel tap. Hence, the explicit values for the fading rate and frequency offset related to any particular channel tap can be extracted from the estimated AR-coefficients pertaining to that particular channel tap.
The fading rate and offset can be used by a receiver in adapting to changing channel conditions, and knowledge of the scattering function generally is advantageous to both a receiver and a transmitter in adapting to changing channel conditions. (A receiver would e.g. change an equalization filter, and a transmitter would e.g. change modulation and coding.)
In current communication systems, the adaptivity of the transmitter and receiver to varying communication channel conditions is limited. As far as is known to the inventor, there does not exist in the prior art any reliable and computationally feasible method for estimating fading rate in case of general multipath fading. For estimating carrier frequency offset, the prior art does teach some methods but the performance of the prior art frequency offset estimation methods in high bit-rate and high mobility applications is generally unknown, and the inventor knows of no prior art teaching of obtaining the offset from a statistical autoregressive model of a communication channel. In particular, the prior art does not teach how to estimate jointly the fading rate and frequency offsets for different multipath signal components in a computationally feasible way.
(In a linear autoregressive model of order R, a time series yn is modelled as a linear combination of R earlier values in the time series, with the addition of a correction term xn:       y    n    model    =            x      n        -                  ∑                  j          =          1                R            ⁢                           ⁢                        a          j                ⁢                              y                          n              -              j                                .                    The autoregressive coefficients aj are fit by minimizing the mean-squared difference between the modelled time series ynmodel and the observed time series yn. The minimization process results in a system of linear equations for the coefficients an, known as Yule-Walker equations. [See Yule, G. U., On a method of investigating periodicities in disturbed series with special reference to Wolfer's sunspot numbers, Phil. Trans. Roy. Soc. Lond. A 226, 267-298; 1927.] Conceptually, the time series yn is considered to be the output of a discrete linear feedback circuit driven by a noise xn, a circuit in which delay loops of lag j have feedback strength aj.)
What is needed is a simple method (or algorithm) for obtaining estimated values for carrier frequency offset (i.e. offset between received carrier frequency and local frequency reference) and also for fading rate, both separately for all resolvable multipath signals, and, ideally, estimated values of parameters characterizing a communication channel generally (i.e. so as to determine a scattering function for the channel) so as to enable improving the radio link between transmitter and receiver by allowing, preferably, both the transmitter and receiver to adapt to changing channel conditions based on the estimated values.